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ACYCLIC COLOURINGS OF PLANAR GRAPHS WITH LARGE GIRTH

Published online by Cambridge University Press:  01 October 1999

O. V. BORODIN ,
A. V. KOSTOCHKA  and
D. R. WOODALL
O. V. BORODIN
Affiliation:
Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090, Russia
A. V. KOSTOCHKA
Affiliation:
Novosibirsk State University, Novosibirsk 630090, Russia
D. R. WOODALL
Affiliation:
Department of Mathematics, University of Nottingham, Nottingham NG7 2RD
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Abstract

A proper vertex-colouring of a graph is acyclic if there are no 2-coloured cycles. It is known that every planar graph is acyclically 5-colourable, and that there are planar graphs with acyclic chromatic number χa = 5 and girth g = 4. It is proved here that a planar graph satisfies χa [les ] 4 if g [ges ] 5 and χa [les ] 3 if g [ges ] 7.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 344 - 352
Copyright
The London Mathematical Society 1999

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